Undergraduate Mathematics Symposium
Saturday, November 2, 2019
University of Illinois at Chicago
Organized by David Dumas, Julius Ross, Christof Sparber, and Kevin Tucker
This page is about the 2019
For the latest symposium information see the UMS home page.
About the symposium
The Undergraduate Mathematics Symposium at UIC is an annual one-day
meeting focusing on undergraduate mathematical research and
education. The meeting features invited lectures by mathematical
researchers, as well as contributed lectures and posters by undergraduates on their own research projects.
Download the symposium poster (designed by Jānis Lazovskis)
- Will Perkins (UIC)
Sphere packings, spherical codes, and hard spheres in high dimensions
What is the densest possible packing of identical spheres in Euclidean space? The answer to this very old question in mathematics is only known in dimensions 1, 2, 3, 8, and 24. In very high dimensions, the answer is almost a complete mystery. I will describe a connection between geometric packing problems such as this and an important probabilistic model from statistical physics: the hard sphere model in which gas molecules are represented by randomly placed non-overlapping spheres. I will then present a new lower bound on spherical codes and kissing numbers in high dimensions.
- Eloísa Grifo (UC Riverside)
Symbolic powers and a story of algebra vs geometry
The equation xy
=0 describes two lines in 2-dimensional space; many
other interesting geometric objects can be described by polynomial
equations. Hilbert's Nullstellensatz gives a correspondence between
such geometric objects, which are called varieties, and the sets of
equations that describe them, which have an interesting algebraic
structure of their own. According to this correspondence, varieties
are described by the polynomials that vanish at precisely all their
points... but how do we measure that vanishing?
We will give some answers, but find that many more questions are still open.
- Benoit Charbonneau (U Waterloo)
The dodecaplex and wonders of the fourth dimension
The dodecaplex is one of the regular solids in four dimensions. I cannot show it to you (the symposium budget doesn't cover extradimensional travel), but can describe many of its features, and show you projections. Prepare for a journey through history and through dimensions.
Transit and parking
The UIC campus is served by the CTA blue line train (UIC-Halsted stop) and many CTA bus lines.
Those driving may use any of the UIC visitor parking lots. Take a
ticket and we can give you a sticker that allows you to exit.
Lectures are held in Lecture Center F4. Plenary lectures are 50 minutes and student lectures 20 minutes.
Registration, lunch, and breaks will all be held in Science and Engineering Offices (SEO) room 300. A catered lunch of sandwiches and salads is provided for all symposium participants.
The main symposium events are all held on Saturday, November 2. We are also offering an optional Friday afternoon poster showing at the UIC math department's weekly tea.
The full schedule of events is as follows:
|Friday, November 1
|4:00 - 5:00pm
||Optional: UMS posters can be displayed at UIC math department tea in SEO 300
|Saturday, November 2
|8:15 - 8:50am
||Sign-in and coffee in SEO 300
|Morning session — Plenary
Lectures — Lecture Center F4
||Will Perkins - Sphere packings, spherical codes, and hard spheres in high dimensions
||Benoit Charbonneau - The dodecaplex and wonders of the fourth dimension
||Eloísa Grifo - Symbolic powers and a story of algebra vs geometry
||Lunch in SEO 300
|Afternoon Session 1 — Student
lectures — Lecture Center F4
||Mary Stelow - Complexity of S-Adic Sequences Associated with Some Multidimensional
||Kelly Chen - Unusual Topographical Features of Laplacian Eigenfunctions
||Talia Blum - Unlikely Intersections and Portraits of Dynamical Semigroups
|Afternoon session 2 — Student
lectures — Lecture Center F4
||Alexandra Newlon - The Fibonacci Quilt Game
||Julinda Mujo - Smocked Metric Spaces and their Tangent Cones
||Dylan King - The Distribution of Missing Sums in Correlated Sumsets
|4:00 - 5:30pm
UMS is supported in part by the following grants from the National Science Foundation: NSF RTG 1246844, DMS 1348092 CAREER.